Signals may be used to transmit data over distances. In optical communication systems, for example, data may be modulated on one or more optical wavelengths to produce modulated optical signals that may be transmitted over optical waveguides such as optical fibers. One modulation scheme that may be used in optical communication systems is phase shift keying (PSK) in which data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength represents symbols encoding one or more bits. A variety of PSK modulation formats are well known. In a binary phase-shift keying (BPSK) format, for example, two phases may be used to represent 1 bit per symbol. PSK formats also include differential phase-shift-keying (DPSK) formats. In a DPSK format, the optical intensity of the signal may be held constant while ones and zeros are indicated by differential phase transitions. DPSK modulation formats include return-to-zero differential phase-shift keying (RZ-DPSK), wherein a return-to-zero amplitude modulation is imparted to a DPSK signal, and chirped return-to-zero differential phase-shift keying (CRZ-DPSK).
PSK formats include a number of known multi-level modulation formats wherein multiple data bits may be encoded on a single transmitted symbol. Examples of multi-level PSK modulation formats useful for encoding two-bits per symbol include: quadrature phase shift keying (QPSK); differential quadrature phase shift keying (DQPSK) wherein information is encoded in four differential phases; and a combination of amplitude shift keying and differential binary phase shift keying (ASK-DBPSK). Multi-level modulation formats with eight symbol levels useful for encoding three bits per symbol include differential 8-level phase shift keying (D8PSK) and ASK-DQPSK. A combination of quadrature amplitude shift keying and differential quadrature phase modulation (QASK-DQPSK) may be used to provide 16 symbol levels, or four bits per symbol. Another alternative modulation format is, namely, quadrature amplitude modulation (QAM), in which information is modulated onto both phase and amplitude of a transmitted signal. For simplicity and ease of explanation, the term “PSK modulation format” refers to any modulation format wherein data is encoded at least in part in the phase of an optical signal, including, but not limited to any of the modulation formats described above.
Since data is encoded in the phase of an optical signal in systems implemented using PSK modulation formats, such systems may include coherent receivers for demodulating the signals. Digital signal processing (DSP) may be implemented in such systems for processing the received signals to provide demodulated data. Digital signal processing of the received signals provides speed and flexibility and may be used to perform a variety of functions including estimation of the carrier phase of the received signals and data detection using the estimated carrier phase. Known methods of implementing carrier phase estimation in a DSP-based coherent receiver have induced unacceptable performance penalties or have required an unacceptably slow initial training period.